We introduce algorithms for optimizing a single-input single-output reconfigurable intelligent surface (RIS) assisted system. The RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances and its reconfigurability is realized through tunable lumped impedances. In the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which accounts for the interplay between the amplitude and phase of the lumped loads of the RIS. In the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling significantly affects the end-to-end received power. If the RIS is optimized by taking the mutual coupling into account, the received power can be increased.

中文翻译：

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可重构智能表面的相互耦合和单元细胞感知优化

我们介绍了优化单输入单输出可重构智能表面 (RIS) 辅助系统的算法。RIS 使用基于互阻抗的电磁兼容框架建模，其可重构性通过可调谐集总阻抗实现。在 RIS 的散射元件之间不存在相互耦合的情况下，我们推导出了最佳可调阻抗的封闭式表达式，它解释了 RIS 集总负载的幅度和相位之间的相互作用。在存在互耦的情况下，我们引入了一种迭代算法来优化 RIS 的可调阻抗。通过证明目标函数不递减且有上界，证明了该算法是收敛的。数值结果表明，互耦合显着影响端到端接收功率。如果通过考虑互耦来优化RIS，则可以增加接收功率。